Connecting cylindrical hallways cleanly
The point is to have the good amount of vertices so that the two can fit easily.

If the cylinder part exposes from top to bottom 9 vertices (ring of 16) then the torus should have 16 minor segments.
Once done,
Boolean approach
Place the two shapes like so, so that they overlap:

Add a boolean union modifier to the torus using the cylinder as object:

Apply it. Cuts should be good but you'll have unwanted vertices:

So delete them.
The result should look good but warning check for doubles and/or overlapping faces (there will be some) and remove them. All should be quad after that.
Knife project approach
Place the cylinder along the torus:

Use a circle of 16 vertices too at the place of the last torus ring:

Keep the circle selected and the cylinder active, in ortho view (like the picture above) and enter edit mode.
Choose the menu &quot;mesh/knife project&quot;. That will make this cut on the cylinder:

Remove these edges and faces:

Join the cylinder and the torus, enter edit mode, select these parts as below and use the menu &quot;edge/bridge edge loops&quot;.

So that the two parts are now connected.
Common part
Now some clean up:
Make the opposite part quad using a knife cut:

Add some bevel using loop cuts CtrlR on these 3 parts: